%0 Journal Article %1 zhang2019hcurltextdollar2textdollarconforming %A Zhang, Qian %A Wang, Lixiu %A Zhang, Zhimin %D 2019 %I Society for Industrial & Applied Mathematics (SIAM) %J SIAM Journal on Scientific Computing %K 35b45-pdes-a-priori-estimates 35q60-pdes-in-connection-with-optics-and-electromagnetic-theory 65n12-pdes-bvps-stability-and-convergence-of-numerical-methods 65n15-pdes-bvps-error-bounds 65n30-pdes-bvps-finite-elements %N 3 %P A1527--A1547 %R 10.1137/18m1199988 %T H(curl\textdollar\^2\textdollar)-Conforming Finite Elements in 2 Dimensions and Applications to the Quad-Curl Problem %U https://epubs.siam.org/doi/10.1137/18M1199988 %V 41 %X In this paper, we construct some $H(curl^2)$-conforming finite elements on a rectangle (a parallelogram) and a triangle. The proposed elements possess some nice properties which have been proved by a rigorous theoretical analysis. Then we apply our new elements to construct a finite element space for discretizing the quad-curl problem. Convergence orders $O(h^k)$ in the $H$(curl) norm and $O(h^k-1)$ in the $H(curl^2)$ norm are established. Numerical experiments are provided to confirm the theoretical results.

@article{zhang2019hcurltextdollar2textdollarconforming, abstract = {In this paper, we construct some $H(curl^2)$-conforming finite elements on a rectangle (a parallelogram) and a triangle. The proposed elements possess some nice properties which have been proved by a rigorous theoretical analysis. Then we apply our new elements to construct a finite element space for discretizing the quad-curl problem. Convergence orders $O(h^k)$ in the $H$(curl) norm and $O(h^{k-1})$ in the $H(curl^2)$ norm are established. Numerical experiments are provided to confirm the theoretical results.}, added-at = {2022-02-17T06:34:46.000+0100}, author = {Zhang, Qian and Wang, Lixiu and Zhang, Zhimin}, biburl = {https://www.bibsonomy.org/bibtex/2cd2d0627243bee54a58532bc62154419/gdmcbain}, doi = {10.1137/18m1199988}, interhash = {b54c7ab29048e1680ba463c675f2499a}, intrahash = {cd2d0627243bee54a58532bc62154419}, journal = {{SIAM} Journal on Scientific Computing}, keywords = {35b45-pdes-a-priori-estimates 35q60-pdes-in-connection-with-optics-and-electromagnetic-theory 65n12-pdes-bvps-stability-and-convergence-of-numerical-methods 65n15-pdes-bvps-error-bounds 65n30-pdes-bvps-finite-elements}, month = jan, number = 3, pages = {A1527--A1547}, publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})}, timestamp = {2022-02-17T06:34:46.000+0100}, title = {H(curl{\textdollar}{\^{}}2{\textdollar})-Conforming Finite Elements in 2 Dimensions and Applications to the Quad-Curl Problem}, url = {https://epubs.siam.org/doi/10.1137/18M1199988}, volume = 41, year = 2019 }